The "N Queens" problem
The "N Queens" problem is a puzzle where you take an NxN chequers or chess board (it's usually 8x8 but this works for the general case) on which you have to place N queens in such a way that none of them threaten or are threatened by any of the others. Reminder: in the game of chess, a queen can move as many squares as she likes horizontally, vertically or diagonally but cannot jump over any of the other pieces on the board like a knight. This means that any piece in her direct line of sight on the same line, in the same column or on a diagonal to her is fair game. With this in mind, it is clear that there is only one solution to the problem on a 1x1 board, i.e. a single square (you just plonk a queen on it and you're done), and that there is no way to organise two queens on a 2x2 board or three queens on a 3x3 board without them threatening each other. For a 4x4 or greater board, there is more than one solution. I thought I'd have a go at solving th...